text: Using Einstein notation, the Navier–Stokes equations for an incompressible fluid in Cartesian coordinates are
  Filtering the momentum equation results in
  If we assume that filtering and differentiation commute, then
  This equation models the changes in time of the filtered variables .  Since the unfiltered variables  are not known, it is impossible to directly calculate .  However, the quantity  is known.  A substitution is made:
  Let . The resulting set of equations are the LES equations: